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- Normal Subgroup Counterexample [closed] 2 answers
Let $H\triangleleft G$, and H is a subgroup of G such that $[G:H] = k$, where $[G:H]$ states the number of left cosets of $H$ in $G$.
1) How may I show that for all $a\in G, a^k\in H$?
2) If we do NOT assume the normality of $H$, can I have any counterexample showing that 1) is not true?